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In this note, we answer a question of Mirzakhani on asymptotic behavior of the one-point volume polynomial of moduli spaces of curves. We also present some applications of Mirzakhani’s asymptotic form...
Asymptotic Formulae.
Asymptotic Formulae for Brillouin Index on Riemannian Manifolds
flat torus Brillouin index geodesic flow topological entropy
2007/12/11
We establish several asymptotic formulae for Brillouin index on flat tori. As an application of these formulae it is proved that the topological entropy of a geodesic flow on a flat torus is zero.